Autozeroing floating-gate amplifier

ABSTRACT

An autozeroing floating-gate amplifier (AFGA) is an integrated continuous-time filter that is intrinsically autozeroing. It can achieve a highpass characteristic at frequencies well below 1 Hz. In contrast with conventional autozeroing amplifiers that eliminate their input offset, the AFGA nulls its output offset. The AFGA is a continuous-time filter; it does not require any clocking. The AFGA includes at least one floating-gate MOS transistor that is capable of hot-electron injection of electrons onto the floating gate of the MOS transistor. Electrons are continuously removed from the floating gate(s), for example, via Fowler-Nordheim tunneling. The AFGA has a stable equilibrium for which this tunneling current is balanced by an injection current of equal magnitude. When the circuit is driven away from its equilibrium by an input or something else, an imbalance between the tunneling and injection current charges (if the tunneling current exceeds the injection current) or discharges (if the injection current exceeds the tunneling current) the floating gate(s) until the equilibrium is re-established. The equilibrium is chosen to achieve a desired baseline of operation.

STATEMENT AS TO RIGHTS TO THE INVENTION

The present invention was made with support from the United StatesGovernment under Grant number N0001489-J-1675 awarded by the Office ofNaval Research of the Department of the Navy and under Grant numberN00014-89-J-3083 awarded by the Advanced Research Projects Agency of theDepartment of Defense. The United States Government has certain rightsin the invention.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of United States Provisional PatentApplication Serial No. 60/004,566 filed Sep. 29, 1995 in the names ofthe inventors hereof and commonly assigned herewith and is a division ofU.S. patent application Ser. No. 08/721,261, filed Sep. 26, 1996 nowU.S. Pat. No. 5,895,126, in the names of the inventors hereof andcommonly assigned herewith.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is directed to a bandpass floating-gate amplifierthat uses tunneling and pFET hot-electron injection so that theamplifier returns to its sensitive region despite large changes in theDC input voltage.

2. The Prior Art

Offsets often present a difficult problem for designers of MOS analogcircuits. A time-honored tradition for addressing this problem is to usea blocking capacitor to eliminate the input DC component; however, forintegrated filters, this approach requires enormous input capacitors andresistors to get time-constants of less than 1 Hz. Existing on-chipautozeroing techniques rely on clocking schemes that compute the inputoffset periodically and then subtract the correction from the input.See, e.g., E. A. Vittoz, "Dynamic analog techniques", in Y. Tsividis andP. Antognetti, Design of MOS VLSI Circuits for Telecommunications,Prentice Hall, 1985. These autozeroing techniques add significantcomplexity to the circuit, as well as clock noise, aliasing, and otherproblems. Accordingly, there is a need for improved autozeroingtechniques and apparatus.

Prior floating-gate transistor devices, which utilize electrical chargestored in a floating polysilicon gate imbedded in an insulator such assilicon dioxide, provide a method of storing analog values as a quantityof electrical charge on an integrated circuit chip. The charge on such afloating gate is known to remain fixed for periods of up to many years.Although the advantages of using floating gate transistors as memoryelements are well known, J. Lazzaro, et al., "Systems Technologies forSilicon Auditory Models," IEEE Micro, Vol. 14, No. 3, 1994, pp. 7-15, T.Allen, et al., U.S. Pat. No. 5,166,562, entitled: "Writable AnalogReference Voltage Storage Device," they have not been used previously toconstruct bandpass amplifiers. The principal reason has been the lack ofa suitable bi-directional mechanism for writing and erasing the offset.Since the gate of a floating gate transistor is completely embeddedwithin an insulator, writing the memory involves moving charge carriersthrough this insulator. Two non-light-based mechanisms are known whichwill move electrons through an insulator. These are tunneling andhot-electron injection. The inherent difficulty in performing theseoperations has been a primary impediment to the implementation offloating gate transistors in such systems.

Transporting electrons across the barrier presented by the silicon/oxideinterface requires that an electron possess more than about 3.1 eV ofenergy. At room temperature the probability that semiconductor electronswill possess this amount of energy is exceedingly small. Alternatively,an electron could tunnel through this barrier; however, at the voltagesand oxide thicknesses used in conventional silicon MOS processing, thetunneling probability is also exceedingly small.

Fowler-Nordheim tunneling involves applying a voltage across the oxidewhich enhances the probability of an electron tunneling through it.Bi-directional oxide currents are required to achieve a balance ofcurrent into or out of a bandpass amplifier. Although the tunnelingprocess has no preferred direction, bi-directional tuneling requireseither dual polarity high voltages, or a single polarity high voltageand a means for pulling the floating gate to this voltage when addingelectrons, and pulling it near ground when removing them. Bothapproaches are unattractive. The dual polarity solution requires anegative voltage much lower than the substrate potential; the singlepolarity solution does not support simultaneous "reading" and "writing".

Single polarity bi-directional tunneling is often used in writingdigital EEPROMs. Since writing the memory involves pulling the floatinggate either to the supply voltage or to ground, the EEPROM cell cannotbe read during the write process. Excess charge is typically added tothe floating gate to compensate for this lack of memory state feedback.Although excess charge is acceptable when writing a binary valued"digital" memory, where the exact quantity of charge is irrelevant onceit exceeds the amount necessary to completely switch the device to oneof its two binary states, uncertainty in the amount of charge applied toan analog device is unacceptable for bandpass amplifier applications.

Hot-electron injection is a process whereby electrons near the surfaceof a semiconductor acquire more than about 3.1 eV of energy, typicallyby acceleration in an electric field, and then surmount thesilicon/silicon-dioxide barrier. Once in the silicon dioxide conductionband, an electric field applied across the oxide carries these electronsto the floating gate. There are a number of ways of accomplishinghot-electron injection.

One source for a high electric field is a depletion region. Forinstance, the collector-to-base depletion region of either a vertical orlateral BJT (bipolar junction transistor) can be used. An example of alateral BJT used in a similar application is shown in U.S. Pat. No.4,953,928 to Anderson, et al. Alternatively, the channel-to-draindepletion region of a high-threshold N-type MOSFET in a moderately dopedsubstrate can be used. An example of such a device used in a similarapplication is shown in U.S. patent application, Ser. No. 08/399,966filed on Mar. 7, 1995 by Diorio, et al. Finally, the drain-to-channeldepletion region of a subthreshold P-type MOSFET can be used.Hot-electron injection in such devices is usually thought of as a sourceof oxide degradation in MOSFETs, Y. Leblebici and S. M. Kang, HotCarrier Reliability of MOS VLSI Circuits, Kluwer Academic, 1993.Nonetheless, this process can be reliably and safely used as a mechanismto adapt the charge stored on a floating-gate MOSFET as shown herein.

Another source for a high electric field is the channel region of asplit-gate N-type MOSFET. Split-gate injectors, as shown and describedin U.S. Pat. No. 4,622,656 to Kamiya, et al., contain two partiallyoverlapping gate regions at very different voltages. The resultingsurface potential drops abruptly at the interface between the two gates,creating a high electric field localized in this small region of thetransistor channel.

SUMMARY OF THE INVENTION

The present invention is directed to a novel device known as anautozeroing floating-gate amplifier (AFGA). The AFGA is an integratedcontinuous-time filter that is intrinsically autozeroing. It can achievea highpass characteristic at frequencies well below 1 Hz. In contrastwith conventional autozeroing amplifiers that eliminate their inputoffset, the AFGA nulls its output offset. The AFGA is a continuous-timefilter; it does not require any clocking. According to the invention, anAFGA includes at least one floating-gate MOS transistor that is capableof hot-electron injection of electrons onto the floating gate of the MOStransistor. Electrons are continuously removed from the floatinggate(s), for example, via Fowler-Nordheim tunneling. The AFGA has astable equilibrium for which this tunneling current is balanced by aninjection current of equal magnitude. When the circuit is driven awayfrom its equilibrium by an input or something else, an imbalance betweenthe tunneling and injection current charges (if the tunneling currentexceeds the injection current) or discharges (if the injection currentexceeds the tunneling current) the floating gate(s) until theequilibrium is re-established. The equilibrium is chosen to achieve adesired baseline of operation.

OBJECTS AND ADVANTAGES OF THE INVENTION

An object and advantage of the present invention is to provide anautozeroing floating-gate amplifier.

Another object and advantage of the present invention is to provide aband pass floating-gate amplifier implemented in an analog MOS circuitand capable of automatically returning to its sensitive regime despitelarge changes in its DC inputs.

Another object and advantage of the present invention is to provideimproved autozeroing photoreceptor circuits.

Another object and advantage of the present invention is to provideimproved autozeroing sensor input circuits.

Another object and advantage of the present invention is to provide anautozeroing differentiator circuit.

Another object and advantage of the present invention is to provide atunable, autozeroing second-order filter which can be cascaded to formsilicon cochleas.

Another object and advantage of the present invention is to provideimproved winner-take-all (WTA) circuits.

Another object and advantage of the present invention is to provideautozeroing floating-gate MOS translinear circuits.

Yet another object and advantage of the present invention is to providean autozeroing, first-order log-domain filter.

These and many other objects and advantages of the present inventionwill become apparent to those of ordinary skill in the art from aconsideration of the drawings and ensuing description of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an electrical schematic diagram of an autozeroingfloating-gate amplifier (AFGA) that uses pFET hot-electron injection.

FIG. 2 is a voltage vs. time response of the AFGA to a 1 Hz sinewavesuperimposed on a 19 s voltage pulse. The AFGA has a closed-loop gain of11.2, and a low-frequency cutoff at 100 mHz.

FIG. 3 shows the effect of drain-to-source voltage on the Early voltageof an nFET and pFET.

FIGS. 4A and 4B depict a small-signal model of a pFET with the effectsof hot-electron injection.

FIG. 5A is a band diagram of a subthreshold pFET transistor underconditions favorable for hot-electron injection.

FIG. 5B is measured data of pFET injection efficiency verses thedrain-to-channel voltage for four source currents.

FIG. 6A shows the steady-state output voltage versus the tunnelingvoltage in an AFGA for three values of V_(t).

FIG. 6B shows the steady-state output voltage versus V_(t) in an AFGAfor two tunneling voltages.

FIGS. 7A-7B shows the response of an AFGA to an upgoing and downgoingstep input. The adaptation in response to an upward step results fromelectron tunneling; the adaptation in response to a downward stepresults from pFET hot-electron injection.

FIG. 8A shows the response of an AFGA to an upgoing and downgoingvoltage step before and after 145 hours of operation.

FIG. 8B shows the extracted device parameters of the AFGA as a functionof time.

FIG. 9A shows voltage vs. time curves for two AFGAs with unity gain asshown, but with each having different values for C₁.

FIG. 9B shows voltage vs. time curves for two AFGAs with differentgains.

FIG. 10A shows the response of three AFGAs to the same square waveinput. Here all three AFGAs were the same except for their values ofC_(w) and were biased by the same V_(t).

FIG. 10B shows the measured linear range and τ_(h) for severalunity-gain AFGAs for different C_(w) ratioed in units of C₁. Both curvesin FIG. 10B are fitted with a linear equation.

FIGS. 11A, B and C depict an AFGA represented as a small-signal circuit.

FIG. 11A shows the small-signal AFGA model using the small-signal pFETmodel.

FIG. 11B shows the small-signal model of the effect of the noise sourcein the channel on the output voltage. The effect of the gate current andthe Early voltage effect has been neglected here.

FIG. 11C shows a simplified small-signal model of the effect of noise.

FIG. 12 shows the frequency response for two AFGAs with different gains.For both the high-and low-gain AFGA, C₁ +C₂ is approximately constant.For the high-gain AFGA, τ₁ is 8 sec, and τ_(h) is 265 μsec; for thelow-gain AFGA, τ₁ is 530 sec and τ_(h) is 4 μsec. The ratio of τ_(h) andτ₁ between the two AFGAs are equal to half of the ratio of the gains,which is consistent with a constant C₁ +C₂.

FIGS. 13A-B depict a noise spectrum of an AFGA for a constant input.

FIG. 13A shows the output noise spectrum of an AFGA with a gain of 146for two different tunneling voltages (V_(tun)).

FIG. 13B shows a comparison of a high-gain AFGA with a unity gain AFGAand a generic follower-connected differential amplifier. All threeamplifiers had the same V_(t) voltage, and correspondingly had the samebias current. The sum of C₁ and C₂ is the same for both AFGAs.

FIG. 14 shows, for an AFGA with a gain of 146, the minimum and maximumoutput voltages verses peak-to-peak output-voltage amplitude. Thefrequency of the input sine wave was 100 Hz.

FIG. 15 shows the response of an above threshold autozero amplifier to aslow downgoing step.

FIG. 16 shows the change in the AFGA output voltage with and without acontinuous tunneling current. An AFGA with a gain of 146 was used foreach case. The case for no tunneling current also required dropping thepower supply; V_(dd) was set at 5V. The trace with no tunneling currentwas taken five minutes after the tunneling line was dropped.

FIGS. 17A-B depict an implementation of an AFGA according to a presentlypreferred embodiment of the present invention in a 2-micron n-well CMOSprocess.

FIG. 17A shows a top plan view of an AFGA device.

FIG. 17B shows a vertical cross-sectional view of the AFGA taken alongline 17B--17B of FIG. 17A.

FIGS. 18A-B show circuits for two autozeroing photoreceptors:

FIG. 18A utilizes a phototransistor and

FIG. 18B utilizes a photodiode.

FIGS. 19A-B show the use of an AFGA with certain generic types ofsensors.

FIG. 20 depicts the circuit of an autozeroing differentiator.

FIG. 21 depicts the circuit of a tunable, autozeroing second-orderfilter which can be cascaded to form silicon cochleas.

FIG. 22 depicts an autoranging winner-take-all (WTA) circuit.

FIG. 23 depicts an autozeroing version of a WTA circuit.

FIGS. 24A-B depict autozeroing floating-gate MOS translinear circuits.

FIG. 25 depicts the circuit for an autozeroing first-order log-domainfilter.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Those of ordinary skill in the art will realize that the followingdescription of the present invention is illustrative only and is notintended to be in any way limiting. Other embodiments of the inventionwill readily suggest themselves to such skilled persons from anexamination of the within disclosure.

Structure of the AFGA

FIG. 1 is an electrical schematic diagram of an autozeroingfloating-gate amplifier (AFGA) 10 that uses pFET hot-electron injectionaccording to a presently preferred embodiment of the present invention.Until now, pFET hot-electron injection has attracted attention only as asource of MOSFET oxide degradation, Y. Leblebici and S. M. Kang, HotCarrier Reliability of MOS VLSI Circuits, Kluwer Academic, 1993,therefore this circuit presents an interesting case of "turning a buginto a feature." The capacitance from the floating gate to ground,C_(w), represents both the parasitic and the explicitly drawncapacitances. Increasing C_(w) will increase the linear input range ofthe circuit. The capacitance connected to the output terminal, C_(L), isthe load capacitance. Between V_(tun) and V.sub.ƒg is the symbol usedherein for a tunneling junction, which is a capacitor between thefloating-gate and an n-well. The open-loop inverting amplifier consistsof a pFET input transistor 12, and an nFET current source 14 which setsthe current through pFET 12. With capacitive feedback, the input signalon line 16 is amplified by a closed-loop gain approximately equal to -C₁/C₂ where C₁ is the value of capacitor 18 and C₂ is the value ofcapacitor 20. The maximum gain is limited both by the open-loop gain,and by the parasitic floating-gate-to-drain overlap capacitance.

The complementary tunneling and hot-electron injection processes adjustthe floating-gate charge in such a way that the amplifier's outputvoltage returns to a steady-state value on a slow time scale (on theorder of a second or longer) when the injection current is equal to thetunneling current. If the output voltage is below its equilibrium value,then the injection current exceeds the tunneling current, decreasing thecharge on the floating gate; that, in turn, increases the output voltageback toward its equilibrium value. If the output voltage is above itsequilibrium value, then the tunneling current exceeds the injectioncurrent, increasing the charge on the floating gate; that, in turn,decreases the output voltage back toward its equilibrium value. Thecircuit behaves like a high-pass filter with a long (≧1 second) timeconstant. The time constant may be set to be arbitrarily long (e.g.,minutes, hours, days, etc.)

A Qualitative Presentation of AFGA Operation

Two conditions must be satisfied for the circuit to be in equilibrium.First, the pFET channel current, I_(p), must be equal to the nFETchannel current I_(n). The quiescent channel current is defined asI_(s0). Second, the injection gate current must be equal to thetunneling current. The quiescent injection current is defined asI_(inj0) which must equal I_(tun0), the quiescent tunneling current, atequilibrium. Since the tunneling and injection currents are many ordersof magnitude smaller than I_(s0) and are charging similarly-sizedcapacitances, the first condition is satisfied much faster than is thesecond condition. The frequency range over which the first condition issatisfied, but the second condition is not satisfied, is where the AFGAbehaves as an amplifier. The combination of electron tunneling and pFEThot-electron injection applies the appropriate negative feedback tostabilize the output voltage such that the second condition is alsosatisfied.

In the frequency range where the first condition does not hold, theoutput voltage is attenuated. In this regime, the circuit behaves as alow-pass filter. Since the output capacitances are charged or dischargedby currents on the scale of I_(s0) the cutoff frequency will be directlydependent on the bias current. Continuous-time integrators operate on asimilar principle, Y. Tsividis, M. Banu, and J. Khaury, "Continuous-timeMOSFET-C filters in VLSI", IEEE Transactions on Circuits and Systems,Vol. 33, No. 2, 1986 and C. Mead, Analog VLSI and Neural Systems,Addison-Wesley, 1989. The AFGA transfer function is bandpass, with thelow-frequency cutoff set by the equilibrium tunneling and injectioncurrents, and the high-pass cutoff independently set by the equilibriumpFET and nFET channel currents.

FIG. 2 shows the response of the AFGA to a 1 Hz sinewave superimposed ona 19 s input voltage pulse. The AFGA has a closed-loop gain of 11.2, anda low-frequency cutoff at 100 mHz.

If the input changes on a timescale that is much faster than theadaptation, then the output is an amplified version of the input signal.The amplifier adapts to the pulse input after an initial transient,while preserving the amplified 1 Hz sine wave.

The AFGA devices discussed herein were fabricated in the 2-micron n-wellOrbit CMOS process available through MOSIS. Typical operating values forV_(tun) were between 33V and 42V; those for V_(dd) were between 6V and12V. Similar data have been obtained with the 1.2-micron n-well OrbitCMOS process, but with typical operating values for V_(tun) between 26Vand 31V. For more modern processes, the typical operating voltages willdecrease, because of thinner gate oxides and higher dopant impurityconcentrations. Those of ordinary skill in the art will realize that anynumber of commercially available process technologies may also be used.

Circuit Model of a pFET With Hot-Electron Injection and ElectronTunneling

Before considering the behavior of the autozeroing amplifier, we firstreview electron tunneling and pFET hot-electron injection. We begin withthe basic subthreshold MOS characteristics, C. Mead, Analog VLSI andNeural Systems, Addison-Wesley, 1989, which are valid even at largedrain-to-source voltages. For subthreshold operation, the change in thenFET channel current for a change in gate voltage, ΔV_(g), around a biascurrent, I_(so), can be described as: ##EQU1## where κ_(n) is thefractional change in the nFET surface potential due to a change inΔV_(g), and U_(T) is the thermal voltage, kT/q. The channel current of apFET is described by: ##EQU2## where κ is the fractional change in thepFET surface potential due to a change in ΔV_(g). Following theconventional definitions of small-signal transconductance, g_(m), andoutput resistance, r_(o), P. Gray and R. Meyer, Analysis and Design ofAnalog Integrated Circuits, Wiley Interscience, 1984, one obtains thefollowing transconductance and output resistance relationships for asubthreshold pFET: ##EQU3##

FIG. 3 shows how the Early voltage, V_(o), changes when the FETs (bothnFETs and pFETs) operate with large drain-to-source voltages. The Earlyvoltage is directly related to the amplifier's open-loop gain; for thisamplifier, the maximum open-loop gain is roughly 200. The Early voltagedecreases at large drain-to-source voltages due to impact ionization inthe drain-to-channel depletion region and holes are accelerated to largeenergies; if a hole has an energy larger than the bandgap, then it mayundergo impact-ionization. The result of an impact ionization is twoholes and one electron. For the nFET biased with a drain-to-sourcevoltage of 3.0V and the pFET biased with a drain-to-source voltage of8.5V, V_(o) is nearly constant for both transistors; therefore theAFGA's open-loop gain also is nearly constant.

FIGS. 4A and 4B depict a small-signal model of a pFET with the effectsof hot-electron injection. Here a constant tunneling current at thefloating gate (V.sub.ƒg) is assumed; this tunneling current sets thebias point for the hot-electron injection parameters.

A. Electron Tunneling

Increasing the tunneling voltage, V_(tun), increases the effectiveelectric field across the oxide, which increases the probability of theelectron tunneling through the barrier. Typical values for the oxidefield range from 0.75V/nm to 1.0V/nm. The classic model of electrontunneling through a silicon/silicon-dioxide system, M. Lenzlinger and E.H. Snow (1969), "Fowler-Nordheim tunneling into thermally grown SiO₂,"J. Appl. Phys., vol. 40, pp. 278-283, 1969, models the electrontunneling current by: ##EQU4## where E_(ox) is the oxide electric field,t_(ox) is the oxide thickness, and E_(o) is a device parameter that isroughly equal to 25.6V/nm, is the starting point of the analysis. C.Mead, "Scaling of MOS Technology to Submicrometer Feature Sizes",Journal of VLSI Signal Processing, 8, pp. 9-25, 1994. As showed in P.Hasler, C. Diorio, B. A. Minch and C. Mead, "Single Transistor LearningSynapses", Advances in Neural Information Processing Systems 7, MITPress, pp. 817-824, 1995. The tunneling current for a fixed bias on thetunneling line is approximated by: ##EQU5## where V_(x) is a parameterrelated to the quiescent tunneling and floating-gate voltages, ΔV_(tun)is the change in the tunneling voltage, and ΔV_(fg) is the change in thefloating-gate voltage from the quiescent floating-gate voltage. For theoperating conditions discussed herein, a typical value of V_(x) is 1Vwith the 42 nm oxide used in the 2-micron n-well Orbit process fromMOSIS.

B. Hot Electron Injection

FIG. 5A is a band diagram of a subthreshold pFET transistor operatingunder bias conditions that are favorable for hot-electron injection.Hot-hole impact ionization creates electrons at the drain edge of thedrain-to-channel depletion region, due to the high electric fieldsthere. These electrons travel back into the channel region, gainingenergy as they go. When their kinetic energy exceeds that of thesilicon/silicon-dioxide barrier, they can be injected into the oxide andtransported to the floating gate. The hole impact-ionization current isproportional to the pFET source current, and is the exponential of asmooth function (ƒ₁) of the drain-to-channel potential (Φ_(dc)). Thisrelationship may be expressed:

    I.sub.impact =I.sub.p e.sup.ƒ.sbsp.1.sup.(Φ.sbsp.dc.sup.)(EQ. 6)

where Φ_(dc) is the potential drop from channel to drain. The injectioncurrent is proportional to the hole impact-ionization current, and isthe exponential of another smooth function (ƒ₂) of the voltage drop fromchannel to drain. This relationship may be expressed:

    I.sub.inj =I.sub.impact e.sup.ƒ.sbsp.2.sup.(Φ.sbsp.dc.sup.)(EQ. 7)

Because the injection current is only a weak function of thefloating-gate voltage for a fixed source current (I_(p)) and Φ_(dc), thegate-voltage dependence may be neglected for this application.

FIG. 5B shows measured pFET injection efficiency for several sourcecurrents (I_(g) =200 nA, 49 nA, 9 nA, 5 nA). Injection efficiency is theratio of the injection current to source current. The injectionefficiencies are nearly identical for the different source currents;therefore, they appear to be indistinguishable on the plot of FIG. 5B.

The functions ƒ₁ and ƒ₂ are approximately linear over a 1 to 2V changein Φ_(dc). With this linear approximation, the hot-electron injectioncurrent may be expressed: ##EQU6## where ΔΦ_(dc) is the change in Φ_(dc)from the quiescent level, and V_(inj) is a measurable device parameter.For a quiescent Φ_(dc) =8.2V, a typical value for V_(inj) is 250 mV. Adecreasing input signal will decrease the pFET surface potential viacapacitive coupling to the floating gate. Decreasing the pFET surfacepotential will increase the source current, thereby decreasing Φ_(dc)for a fixed output voltage, and lowering the injection efficiency.Consequently as derived in P. Hasler, C. Diorio, B. A. Minch, and C.Mead, "Single Transistor Learning Synapses", Advances in NeuralInformation Processing Systems 7, MIT Press, pp. 817-824, 1995, theinjection current may be modelled as the α power of the source currentas follows: ##EQU7## where I_(so) is the quiescent source current, V_(d)is the drain voltage, and α is 1-U_(T) /V_(inj). A typical value of α is0.90, which is consistent with V_(inj) equal to 250 mV.

The small-signal quantifies g.sub.ƒg and r.sub.ƒg which are both shownin FIG. 4B can now be expressed, using EQ. 5 and EQ. 9. The termg.sub.ƒg is defined as the change in the gate current in response to achange in drain voltage. Because only the injection current depends uponthe drain voltage, g.sub.ƒg =I_(tun0) /V_(inj). The term r.sub.ƒg isdefined for a pFET as the negative change in gate current for a changein gate voltage. Because the effects of both the tunneling and thehot-electron injection processes need to be included, the model forr.sub.ƒg is ##EQU8## where x∥y=xy/x+y. Equilibrium Voltages of the AFGA

Qualitatively, two factors change the steady-state output voltage. Forthe injection current to match the tunneling current after a change inV.sub.τ or V_(tun), the output voltage must reach a new equilibrium.Increasing the bias voltage or channel current requires an increase inthe output voltage, because the pFET must reduce its injectionefficiency so that the injection current matches the original tunnelingcurrent. Increasing the tunneling voltage, which increases thesteady-state tunneling current, requires a decrease in the outputvoltage, because the pFET must increase its injection efficiency so thatthe injection current matches the new tunneling current.

Above, two conditions for equilibrium were postulated; they are nowdescribed quantitatively. Assuming an initial operating point, andconsidering changes in the steady-state output voltage in response to achange in V.sub.τ or in V_(tun), the current in the nFET must be equalto the current in the pFET: ##EQU9## where ΔV.sub.τ is the change in thebias voltage, and ΔV_(fg) is the change in the pFET's floating-gatevoltage. Therefore, the following relation is obtained:

    ΔV.sub.fg =-K.sub.n /KΔV.sub.τ             (EQ. 11)

Qualitatively, the bias current in the nFET sets the current in thepFET, and therefore sets the floating-gate voltage.

Second, the tunneling current must be equal to the injection current:##EQU10## Here, if it is assumed that I_(inj0) is equal to I_(tun0) atthe initial operating point, the second equilibrium relationship isobtained: ##EQU11## For above-threshold operation, the above equationbecomes ##EQU12##

FIGS. 6A-6B show the measured change in the steady-state output voltageversus circuit parameters. Both data sets agree with the model describedin EQ. 13. The AC gain of this amplifier was 146. FIG. 6A shows thesteady-state output voltage versus the tunneling voltage for threevalues of V.sub.τ. FIG. 6B shows the steady-state output voltage versusV.sub.τ for two tunneling voltages (36.35V, 36.9V). The curves begin tosaturate for above-threshold bias currents, as predicted by EQ. 14.

An ideal amplifier is insensitive to variations in the bias voltages;the data in FIGS. 6A-6B show the circuit's DC sensitivity to V.sub.τ andV_(tun). First, the DC gain from the tunneling node to the output isgiven by V_(inj) /V_(x), which, for the measured data shown, is 0.64.The DC gain from the nFET gate to the output is given by ##EQU13##which, for the measured data shown, is 10. The DC gain from the input tothe output is zero. All three gains are smaller than the AFGA AC gain of146.

Under the proper bias conditions, the power-supply rejection depends onthe choice of reference. With the input and output referred to V_(dd),and with V.sub.τ referred to GND, the AFGA gain from the power-supply tothe output is 0.1, which results in a passband power-supply rejectionratio of 64 dB. The power-supply rejection ratio is limited by theopen-loop gain of the amplifier. If instead all nodes are referred toGND, the AC power supply gain is 146, which decreases the passbandpower-supply rejection ratio to 0 dB. The circuit designer must also becareful of where the floating-gate capacitances are connected; for goodpower supply rejection, all these capacitors must be referenced toV_(dd). Otherwise, the power supply becomes another input to the AFGAand any AC power supply noise will appear at the output, amplified bythe AFGA's AC gain.

The steady-state output voltage and the high-pass cut-off frequency areset explicitly by V_(tun) and by the power-supply voltage. IncreasingV_(tun) increases the tunneling current, which in turn decreases thesettling time, but it also decreases the steady-state output voltage,since the pFET must have a larger drain-to-source voltage. Increasingthe power-supply voltage decreases the tunneling current by decreasingthe voltage across the oxide, increasing the settling time andincreasing the steady-state output voltage.

Low Frequency AFGA Behavior

Two general equations can be written which govern the autozeroingfloating-gate amplifier behavior around an equilibrium output voltage.The first equation is obtained by applying Kirchoff's current law (KCL)at the floating gate: ##EQU14## The second equation is obtained byapplying KCL at the output node: ##EQU15## This neglects the Earlyeffect, which adds a correction term to EQ. 16. As long as theclosed-loop gain is much lower than the amplifier gain, ignoring theEarly effect is a good approximation.

In the passband, where the AFGA is an amplifier, the floating gate isheld nearly fixed by the amplifier feedback, and the tunneling andinjection currents are negligible. This approximation simplifies EQ. 15to ##EQU16## thus, the change in the output voltage (ΔV_(out)) is equalto the input voltage (ΔV_(in)) amplified by -C₁ /C₂.

A. Low-Frequency Model

Two approximations are made here to model the low frequency response ofthe AFGA. First, the open-loop gain from the floating gate to the outputcan be large; a typical value is 700. To keep the output voltage betweenthe supply rails, the floating gate voltage is confined to a 10 mVswing. Thus, the floating-gate voltage is approximated by a constantvalue. Second, because the floating-gate voltage is nearly constant, thesource current varies only slightly. The quiescent source current(I_(s0)) is set by the nFET current source. From EQ. 5 and EQ. 9, themodel of injection current for a fixed source current I_(s0) istherefore: ##EQU17## where I_(tun0) =I_(inj0) for the circuit inequilibrium. Since the floating gate is held nearly constant byfeedback, the floating-gate voltage dependence in EQ. 9 is negligible.Even when the circuit is biased with above-threshold currents, thetunneling current still is nearly fixed. Since the injection efficiencyis still an exponential function of the drain voltage forabove-threshold currents, the low-frequency dynamics are similar inbelow- and above-threshold operation.

With the above approximations, the amplifier's output voltage, V_(out),can be modeled in terms of V_(in), with a single equation. The totalfloating-gate current is the sum of the capacitive currents of the inputand output terminals, plus the tunneling and injection currents. FromEQ. 15: ##EQU18## To solve EQ. 19, make the following change ofvariables: ##EQU19## The resulting equation for X is a linear,first-order differential equation with variable coefficients ##EQU20##where τ₁, the low-frequency cutoff, is equal to C₂ V_(inj) /I_(tun0),and A_(v) is the closed-loop AC gain of the amplifier, -C₁ /C₂.

B. Response to a Voltage Step

Consider the AFGA's response to an input voltage step. Assume that theoutput voltage has adapted initially to its steady-state value. To solveEQ. 21, first assume that the output voltage immediately after applyingthe step, ΔV_(out) (0⁺), is given by the magnitude of the input steptimes the AFGA AC gain. Employing ΔV_(out) (0⁺) as a new, effectiveinitial condition, and denoting the effective initial condition in X by:##EQU21## For a downward step, X(0⁺) is greater than 1; for an upwardstep, X(0⁺) is less than 1. After the input step, dV_(in) /dt=0;therefore EQ. 21 becomes: ##EQU22## The solution to EQ. 23 in terms ofΔV_(out) is ##EQU23## where ΔV_(out) →0 as t→∞.

The step response has three interesting regimes, which are approximatedby ##EQU24## The first case occurs when the tunneling current is nearlyequal to the injection current just after the voltage step. The solutionin this region is the familiar exponential decay of a linear system. Thesecond case occurs when the tunneling current dominates the injectioncurrent. The behavior of the output voltage in this regime results fromthe constant tunneling current removing electrons from the floatinggate. The third case occurs when the injection current dominates thetunneling current.

FIGS. 7A-7B shows the response of the AFGA to an upgoing and downgoingstep input. The adaptation in response to an upward step results fromelectron tunneling; the adaptation in response to a downward stepresults from pFET hot-electron injection. This amplifier had a gain of11.2. FIG. 7A shows a plot of the curve fits of the simplifiedexpressions of EQ. 25, where either tunneling or injection dominates therestoration process. From the fits, τ₁ is 4.3 s and I_(tun0) is 50 ƒA.The value of τ₁ can be set reliably to more than 10⁵ seconds. FIG. 7Bshows the response to a square wave for four different values (41V,40.5V, 40V, 39.5V) of the tunneling voltage. This amplifier of FIG. 7Bhad a gain of 147; the input square wave is not shown. The steady-stateoutput voltage decreased in the same manner as seen in FIG. 6B forincreasing tunneling voltages. The initial tail in the upgoing responseis due to the output voltage going to ground. FIG. 7A shows a measuredresponse to an input pulse, with curve fits to the regions here eitherthe tunneling or injection current dominates.

C. Long-Term Parameter Drift

The physical properties of the tunneling and hot-electron injectionmechanisms change with time. These processes are permanently modified aselectrons pass through the oxide, creating electron traps. The long-termchanges were investigated by performing an accelerated stressexperiment, where an AFGA was continuously operated for 145 hours withan average τ₁ of 1.7 s. When used as an amplifier or as a low-passfilter, a more reasonable τ₁ would be at least several minutes;therefore, this experiment is equivalent to the stress of operating theAFGA continuously for a few years. The effect of an input signal onlyslightly modifies the results of this experiment. To characterize thebehavior of the AFGA over time, a similar square wave experiment to theone shown in FIGS. 7A-7B was performed once per hour for 145 hours. Toeach of the resulting output waveforms, the expressions of EQ. 25 werefit and the relevant device parameters were extracted.

FIGS. 8A and 8B show the effect of operating an AFGA for a long time. InFIG. 8A the response to an upgoing and downgoing voltage step before andafter 145 hours of operation is shown. The difference in the outputvoltage from its equilibrium DC level is plotted as a function of time;the equilibrium output voltage slightly increased from the 145 hours ofoperation. In FIG. 8B the extracted device parameters as a function oftime are shown. Since I_(tun0) /C₂ changes more than V_(inj), one cansee that most of the long term change is due to the tunneling junction,which is probably due to oxide trapping.

High-Frequency AFGA Behavior

For sufficiently high frequencies, the AFGA is a low-pass filter. Inthis regime, the tunneling and injection currents are negligible;therefore EQ. 15 is approximated by: ##EQU25## From EQ. 26, changes inV_(out) are proportional to changes in V.sub.ƒg and V_(in). At extremelyhigh frequencies, the transistor channel currents are negligiblecompared to the capacitive currents. In this capacitive-feedthroughregime, the solutions to EQ. 16 and EQ. 26 are ##EQU26## The effects ofthe capacitive feedthrough can be reduced by increasing either C_(L) orC_(w).

At frequencies between the low-frequency cutoff and thecapacitive-feedthrough regime, the behavior of the AFGA results from thefloating-gate voltage settling back to its equilibrium value. Therefore,combining EQ. 16 and EQ. 26 into a single equation for the floating-gatevoltage: ##EQU27## This equation is similar to EQ. 21, which describesthe output-voltage response in the low-frequency case. Substituting:##EQU28## into EQ. 28 results in the linear differential equation:##EQU29## where τ_(h2) is defined to be: ##EQU30## which is the timeconstant that marks the onset of capacitive feedthrough. Defining τ_(h): ##EQU31## which represents the high-frequency cutoff.

As in the low-frequency case, the response to an input voltage step willbe considered. To solve EQ. 30, first assume that the floating-gatevoltage immediately after applying the step, ΔV_(fg) (0⁺), is given bythe magnitude of the input step attenuated by the capacitive dividerratio, EQ. 27. With this initial condition, the solution is: ##EQU32##After the initial jump, given by EQ. 27, the output voltage is relatedto the floating-gate voltage by: ##EQU33##

FIGS. 9A-9B show the high-frequency AFGA behavior. In FIG. 9A, voltagevs. time curves for two AFGAs with unity gain are shown, but with eachhaving different values for C₁. The larger-capacitor circuit had C₁ =C₂=300ƒF, whereas the smaller-capacitor circuit had C₁ =C₂ =50ƒF. For bothAFGAs, C_(L) was the same. The two AFGAs are operating the differentsubthreshold bias currents in order to achieve comparable settlingtimes. As in the low-frequency case, the high-frequency response of theAFGA is asymetric: the downgoing step response approaches its steadystate linearly with time, and the upgoing step response approaches itssteady state logarithmically with time. The initial jump in thedowngoing step is due to capacitive feedthrough. From these data, it isevident that decreasing C₁ and C₂ without changing C_(L) will decreasethe amount of capacitive feedthrough. FIG. 9B shows the voltageresponses to a small input step for two AFGAs with respective gains of 1and 146. The response from the unity-gain AFGA (at the bottom) shows alinear, first-order, low-pass filtered version of the input. Theseresponses illustrate the gain-bandwidth tradeoff in the AFGA.

The linear 3V output swing in the high-gain response of FIG. 9B raisesthe question: What determines the linear range of an AFGA? The criterionfor linearity is that ΔV_(fg) be sufficiently small that the factor,##EQU34## in EQ. 28 can be approximated by -κΔV_(fg) /U_(T). Thiscriterion implies that the floating-gate voltage must not move by morethan U_(T) /κ from its equilibrium value. The floating-gate voltage hasits maximum swing in the capacitive-feedthrough regime; therefore, fromEQ. 27 the input linear range, V_(Li), is ##EQU35## where: ##EQU36## Foramplifiers with gains greater than or equal to one, which requires thatC₁ be greater than C₂, B is bounded between 1/2 and 1 for all C₁, C₂,C_(w), and C_(L). Further, if the AFGA is driving a C_(L) that is atleast as big as C₁, B is bounded between 3/4 and 1. Consequently, B canbe considered a correction term.

The output linear range, V_(Lo), is expressed in terms of the inputlinear range, V_(Li), by: ##EQU37## which is V_(Li) times the amplifiergain, C₁ /C₂. The output linear range scales with the amplifier gain. Byincreasing C_(w), the change in the floating-gate voltage can bereduced, thereby increasing the amplifier's output linear range. TheAFGA's gain from input to output in the passband is: ##EQU38## where Ais the gain from floating gate to output. For a sufficiently large A,the AFGA's passband gain is independent of C_(w).

FIGS. 10A-B show the linear range of the AFGA versus C_(w). In FIG. 10Athe response of three AFGAs to the same square wave input is shown. Hereall three AFGAs were the same except for their values of C_(w) and werebiased by the same V_(t). Increasing C_(w) increases the linear range,decreases the amount of capacitive feedthrough, and decreases thelow-pass cutoff frequency. FIG. 10B shows the measured linear range andτ_(h) for several unity-gain AFGAs for different C_(w) ratioed in unitsof C₁. Both curves in FIG. 10B are fitted with a linear equation. For aunity gain AFGA, that is C₁ =C₂, the expressions for τ_(h) and inputlinear range are: ##EQU39## The data in FIGS. 10A-B was taken with AFGAsthat had no explicitly drawn C_(L) ; the variation between the data andthe linear curve fit is most likely due to the different parasitic loadcapacitances. Both from experimental data and the direct analyticsolution of EQ. 30, second harmonic distortion dominates for the AFGAs;for a sine-wave input with amplitude of V_(Li), the peak second harmonicdistortion is 0.05 percent of, or 26 dB below, the fundamental frequencyresponse. The second harmonic distortion is maximum for frequencies justbelow 1/2 πτ_(h) ; for amplitudes at or below V_(L), the second harmonicdistortion is proportional to the square of the fundamental amplitude.

Frequency Response of the AFGA

In order to derive the AFGA frequency response, one begins with thesmall-signal form of EQ. 15 and EQ. 16: ##EQU40## that is, one assumesthat the input signal is sufficiently small that one needs to keep onlythe linear terms when expanding the exponentials. A small-signal inputchanges V_(out) by less than V_(inj), due to the injection nonlinearityin the low-frequency regime, and V.sub.ƒg by less than U_(T) /κ, due tothe transistor nonlinearity in the high-frequency regime.

FIGS. 11A-C depict an AFGA represented as a small-signal circuit. FIG.11A shows the small-signal AFGA model using the small-signal pFET model.FIG. 11B shows the small-signal model of the effect of the noise sourcein the channel on the output voltage. The effect of the gate current andthe Early voltage effect has been neglected here. FIG. 11C shows asimplified small-signal model of the effect of noise. For clarity, wedefine ##EQU41## EQ. 41 can also be obtained by analyzing thesmall-signal circuit in FIG. 11A. The response in the low-frequency andhigh-frequency regimes, which typically do not interact will bediscussed in turn. Finally, the general solution will be presented.

For low-frequency inputs, one can approximate EQ. 41 as: ##EQU42## forwhich the resulting frequency response is: ##EQU43##

For high-frequency inputs, one can simplify EQ. 41 by assuming inputfrequencies much larger than 1/2 πτ₁, which are written: ##EQU44## Thistransfer function includes the effects of parasitic and loadcapacitances. The response in EQ. 44 is the transfer function of afirst-order system; because capacitive feedback is used, the AFGA isstable for any value of closed loop gain. As seen in FIG. 12, τ_(h) is265 μsec for the high-gain AFGA, and τ_(h) is 4 μsec for the low-gainAFGA.

The response for all frequencies is obtained by taking the Laplacetransform of EQ. 41, which is ##EQU45## EQ. 45 is solved to obtain:##EQU46## where τ₁, τ_(h), τ_(h2) were defined previously.

FIG. 12 shows the frequency response for two AFGAs with different gains.The high-gain AFGA has a gain of 146, and the low-gain AFGA has unitygain. For both the high and low-gain AFGA, C₁ +C₂ is approximatelyconstant. For the high-gain AFGA, τ₁ is 8 sec, and τ_(h) is 265 μsec;for the low-gain AFGA, τ₁ is 530 sec and τ_(h) is 4 μsec. The ratio ofτ_(h) and τ₁ between the two AFGAs are equal to half of the ratio of thegains, which is consistent with a constant C₁ +C₂.

When considering the frequency response of the AFGA, it is natural toconsider the output-voltage spectrum for no input--that is, the outputvoltage noise from the amplifier. FIGS. 13A-13B show AFGA output-voltagespectrums for a fixed voltage-source input. For low frequencies, 1/ƒnoise is dominant, and for high frequencies, thermal noise dominates.The AFGA filters the 1/ƒ noise below the low-frequency cutoff.

FIGS. 13A-B depict a noise spectrum of an AFGA for a constant input.FIG. 13A shows the output noise spectrum of an AFGA with a gain of 146for two different tunneling voltages (V_(tun)). The high-frequencycutoff eliminates 1/ƒ noise at frequencies below 1/τ_(l), The spectrumwas taken for a bias current of 80 nA, which corresponds to V_(t) of0.73 V. FIG. 13B shows a comparison of a high-gain AFGA with a unitygain AFGA and a generic follower-connected differential amplifier. Allthree amplifiers had the same V_(t) voltage, and correspondingly had thesame bias current. The sum of C₁ and C₂ is the same for both AFGAs. FIG.13A shows that we can reduce the 1/ƒ noise by increasing V_(tun), andthereby decreasing τ₁. FIG. 13B shows a comparison between a high-gainAFGA, a unity gain AFGA, and a follower-connected transconductanceamplifier. The transconductance amplifier is the wide-range amplifier asdescribed in C. Mead, Analog VLSI and Neural Systems, Addison-Wesley,1989; it has larger transistors than do the AFGAs, resulting in thelower 1/ƒ noise in FIG. 13B. The AFGAs used a constant tunnelingcurrent; therefore, we conclude that the tunneling and injectionprocesses do not significantly contribute to the noise levels.

It is of interest to investigate how changing the AFGA design willchange the amount of output noise. Following Rahul Sarpeshkar, TobiasDelbruck, and Carver A. Mead, "White Noise in MOS Transistors andResistors," IEEE Circuits and Devices, November 1993, pp. 23-29., onecan model the thermal noise component, 1_(o) of a subthreshold MOSFET'schannel current by: ##EQU47## Because the AFGA's output comprises bothan nFET and a pFET, the total thermal-noise current derives from twoparallel noise sources. To find the output-referred voltage noise, thesimplified small-signal circuit of FIG. 11B can be used. Thesmall-signal circuit of FIG. 11B can be further simplified to that shownin FIG. 11C, by noting that one can relate V.sub.ƒg to V_(out) by acapacitive divider. From this simpler circuit, we express the signalpower of the output-referred voltage noise, V² _(out) can be expressedas: ##EQU48## where τ_(h) was defined above. From this expression, thetotal-output-noise power is: ##EQU49## which, using EQ. 32 evaluates to:##EQU50## with the correction term, B, as defined in EQ. 36. Thetotal-output-noise power is roughly proportional to C_(w) and inverselyproportional to C_(L). R. Sarpeshkar, R. F. Lyon, and C. Mead, "Alow-power wide-linear-range transconductance amplifier", AnalogIntegrated Circuits and Signal Processing, in Press. See also, U.S. Pat.No. 5,463,348 entitled "CMOS Low-Power, Wide-Linear-Range, Well-InputDifferential and Transconductance Amplifiers".

To calculate the dynamic range of an AFGA one may define the dynamicrange (DR) in terms of signal power as the ratio of the maximum possibleoutput swing corresponding to the input linear range and an input thathas an equivalent swing to the total-output-noise power. With thisdefinition, which is equivalent to EQ. 12, we can express the dynamicrange for the AFGA as: ##EQU51## which is a similar form for dynamicrange for the wide-linear-input-range amplifier discussed in R.Sarpeshkar, R. F. Lyon, and C. Mead, "A low-power wide-linear-rangetransconductance amplifier", Analog Integrated Circuits and SignalProcessing, in Press. See also U.S. Pat. No. 5,463,348 entitled "CMOSLow-Power, Wide-Linear-Range, Well-Input Differential andTransconductance Amplifiers". Like the wide-linear-input-rangeamplifier, this amplifier increases dynamic range by amplifying thesignal more than the total amplifier noise. The cost for thisperformance enhancement is a proportional increase in the powerdissipation. Another direct result of this expression is that thedynamic range varies inversely with C₂ ; therefore, a high-gainamplifier will have a larger dynamic range than the low-gain amplifierfor the same C₁, C_(w), and C_(L).

Steady-State Output-Voltage Dependence On The Output Signal

In this section, the dependence of the steady-state output voltage onthe amplitude of the input signal is discussed. Consider the range offrequencies in which the input voltage changes at a rate that is muchslower than the circuit's integrating behavior, but is much faster thanthe adaptation due to the tunneling and injection currents; that is, theinput is entirely in the AFGA's passband.

FIG. 14 shows measurements of the minimum and maximum output voltagesversus output amplitude. For small input amplitudes, the minimum andmaximum output symmetrically diverge from the steady-state voltage, butfor large input amplitudes, most of the change in the output voltage isdue to the maximum of the output voltage increasing. In general, thesteady-state output voltage converges to within about V_(inj) of theminimum of the signal.

To analyze this effect, we decompose the output voltage into componentsthat change at fast and slow rates. We assume that we can express theoutput voltage as a sum of fast and slow variables; that is:

    ΔV.sub.out =ΔV.sub.out +ΔV.sub.out       (EQ. 51)

where ΔV_(out) represents the fast-timescale behavior, and is theamplified version of ΔV_(in) (ΔV_(out) =-C₁ /C₂ ΔV_(in)), and ΔV_(out)represents the slow-timescale behavior. With this formulation, EQ. 51can be integrated over a large number of periods of the fast timescale,but can still make only a small change in the slow-timescale outputvoltage. E[.] shall mean the average of a time-varying signal, x(t),over a time interval, T, that is sufficiently shorter than the slowtimescale, but is much longer than the shortest period of the fastvariables: ##EQU52## By this definition, ##EQU53## The resultingequation in ΔV_(out) is ##EQU54## Expressing ##EQU55## in terms of thefast and slow variables: ##EQU56## Rewriting EQ. 54 as: ##EQU57## Fromthe analysis above, the solution to EQ. 54 is: ##EQU58## where thesteady state solution for ΔV_(out) is: ##EQU59## The amplifier alwaysadapts such that the minimum of the output signal always returns to theequilibrium output voltage.

Now, consider the behavior of the output voltage as a function ofdifferent amplitude sine waves applied to the input. The version of theinput signal after it is amplified by the AFGA is defined as ΔV_(out) =Asin (ωt); for this output signal, the steady state voltage is: ##EQU60##

FIG. 14 shows, for an AFGA with a gain of 146, the measured minimum andmaximum output voltages verses peak-to-peak output-voltage amplitude.The frequency of the input sine wave was 100 Hz. For small inputamplitudes, the minimum and maximum output voltages symmetricallydiverge from the steady state voltage, but for large input amplitudes,most of the output voltage change follows the maximum output voltage.The DC voltage was fit to the function 0.25 ln (0.667+0.333exp(V_(dc)/0.62)), which is nearly equal to EQ. 60.

Other AFGA Effects

A. Modeling the Above-Threshold AFGA

The operation of an autozeroing floating-gate amplifier operating withabove threshold bias currents does not change from the subthreshold casein three important respects. First, those effects that depend onelectron tunneling remain the same, because tunneling is not a functionof the MOSFET channel current. Second, the injection current is stillthe exponential of roughly the same function of the drain voltage.Third, the low frequency dynamics should remain unchanged for a constantC₂, because the channel current is still nearly fixed by feedback.

The pFET hot-electron injection model changes for above-threshold biascurrents in two ways. First, the source current is not an exponentialfunction of the gate voltage, but varies quadratically with the gatevoltage. Second, although operating the AFGA above threshold has littleeffect on the hot-electron-injection efficiency, the injectioncurrent/source current efficiency will decrease above threshold becausethe impact-ionization efficiency will decrease, because the channelpotential decreases near the drain edge with decreasing gate voltage.The above-threshold injection-current model from EQ. 9 can be modifiedto be: ##EQU61## This model modifies the DC output voltage, as mentionedabove, to be: ##EQU62## Recall from FIG. 6, that the equilibrium outputvoltage versus the bias current began to saturate for above-thresholdbias currents.

Now consider how the high frequency behavior changes for above-thresholdbias currents. For above-threshold currents, EQ. 28 is modified to:##EQU63## The definitions of τ_(h) and τ_(h2) are similar to theirsubthreshold definitions, ##EQU64## The higher bias current results in ahigher cutoff frequency, but also requires an increase in powerdissipation. The linear input range of the amplifier is larger than itis for subthreshold bias currents. The linear input voltage range is##EQU65## The large-signal dynamics change for above threshold biases,when the input voltage exceeds its linear range. Thefloating-gate-to-drain capacitance is a function of the drain voltage,which adds additional dynamics to the large signal response.

FIG. 15 shows the response of an above threshold autozero amplifier to aslow downgoing step. The capacitance of the floating-gate changes withthe output voltage due to the change in the capacitance between theoutput and the floating gate.

B. Continuous Operation of the Tunneling Current

It is of interest to understand what happens when a continuouslyoperating tunneling current is not present in the AFGA. The constanttunneling bias current naturally eliminates the effect of DC biasingpoints; without this current, the circuit is no longer an autozeroingamplifier. Without the constant tunneling current, circuitry must beadded to remove the effect of the DC input voltage. Furthermore,additional 1/ƒ noise is generated in this floating-gate amplifier, sincethe high-pass behavior, due to the floating-gate adaptation, filters outa substantial amount of 1/ƒ noise.

Assume that one wants to autozero the floating-gate amplifier only toset a particular operating point. Then, after this calibration phase,one needs to lower the tunneling voltage and power supply to turn offthe electron-tunneling and hot-electron-injection processes to eliminatethe oxide currents. Unfortunately, the capacitive coupling of thetunneling junction and capacitances not referenced to V_(dd) to thefloating gate will make potentially large changes in the output voltage.This effect can be minimized by using small tunneling junctions and byensuring that all the capacitances (including all parasitics) couplinginto the floating gate are referenced to V_(dd).

In addition to the capacitive coupling, the charge on the floating gatewill change due to electron traps in the oxides. When tunneling orinjecting electrons into SiO₂, a portion of these electrons will becometrapped in the oxide, E. H. Nicollian and J. R. Brews, MOS Physics andTechnology, Wiley Interscience, 1982. In addition, as more currentpasses through these oxides, more electron traps are created, C. Hu, S.Tam, F. Hsu, P. Ko, T. Chan, and K. Terrill, "Hot-Electron-InducedMOSFET Degradation-Model, Monitor and Improvement", IEEE Transactions onElectron Devices, Vol. ED-32, No. 2, February 1985, pp. 375-385. Afterthe oxide currents stop, some of these trapped electrons will becomefree thermally, and will find their way to the floating gate. Thiseffect will result in a large drift in the output voltage over time forthe same input bias voltage.

FIG. 16 shows the change in the AFGA output voltage with and without acontinuous tunneling current. An AFGA with a gain of 146 was used foreach case. The case for no tunneling current also required dropping thepower supply; V_(dd) was set at 5V. The trace with no tunneling currentwas taken five minutes after the tunneling line was dropped. The changein the output voltage over time for a high-gain AFGA with and without aconstant tunneling current is shown in FIG. 16. The detrapping effect inthis high-gain AFGA shows no sign of stopping until the output runs intoground; in a lower-gain circuit, the detrapping may eventually settleout within the power supply.

C. Restoration to Equilibrium of an Output Voltage when Starting at theVoltage Rails

What happens when the output voltage starts at one of the supply rails?The output voltage starts at V_(dd) when the floating-gate voltage istoo low. In this regime, there is no injection current, and thetunneling current removes electrons from the floating gate, raising thefloating-gate voltage. Eventually, the floating-gate voltage increasesto its steady-state level, and the output voltage decreases from V_(dd).If the output voltage starts near ground, then the pFET cannot getsufficient channel current to develop enough injection to balance thetunneling current. The current must be balanced by changes in thefloating-gate voltage: in this case, the floating-gate voltage willincrease, since the tunneling current is stronger than the pFETinjection current. Unfortunately, the resulting pFET channel currentwill decrease even further, and that will decrease the injectioncurrent, leading to a runaway condition. The steady-state output voltagemay not return to the original equilibrium level. Typically, thiscondition poses no problem even for reasonably large changes in theinput voltage; however, this effect is seen when large changes inV.sub.τ are made. Decreasing V_(tun), decreasing the input voltage,increasing V.sub.τ, or increasing V_(dd) might allow the AFGA to recoverfrom this condition.

An Implementation Of An AFGA In Silicon

An AFGA has been constructed in a standard 2-micron, double-poly,n-well, CMOS process. The device is shown in FIGS. 17A and 17B. Typicaldopant levels used in this implementation are as follows: for p⁺ and n⁺active regions, 10¹⁹ to 10²⁰ cm⁻³ ; for n⁻ well regions, 10¹⁶ cm⁻³ ; forp⁻ substrate, 5×10¹⁵ cm⁻³. The field oxide is usually between 0.5 and1.0 microns thick and the gate oxide is usually 400 Å thick.

FIG. 17A shows a top plan view of the AFGA. With the exception of theminimum-width finger 100 that extends out to the tunneling junction 102from the floating gate pFET 104, the polysilicon floating gate 106 ispreferably completely surrounded by an n⁻ well 108 in order to maximizepower supply rejection. The high-voltage (typically +35 to +40 volts DC)tunneling well is typically placed at least 15 microns from the nearestwell in order to ensure that the depletion regions surrounding the wellsdo not punch through. The ratio of the area of input capacitor C₁ (110),to the area of the feedback capacitor, C₂ (112), determines the AFGA'sclosed loop passband AC gain, which is ideally equal to -C₁ /C₂ (i.e.inverting). The nFET 114 and pFET 116 transistors shown are both 6microns wide and 9 microns long; however, those dimensions are notcritical. The length of each transistor determines its Early voltage.These parameters, in turn, determine the open-loop gain of theamplifier; the greater the open-loop gain of the amplifier, the moreaccurate the closed-loop passband gain. The width of the pFET determinesthe size of the parasitic floating-gate-to-drain overlap capacitance(about 0.1 fF/μm of floating-gate-to-drain overlap). The size of thisparasitic capacitance compared to the size of the feedback capacitor, C₂(112), (about 0.5 fF/μm² of poly 1-poly 2 overlap) also determines theaccuracy of the AFGA's closed-loop passband gain. The size of thecapacitance from V_(dd) (power supply at approximately +12 volts (arange of about +7 VDC to about +15 VDC is presently preferred)) to thefloating-gate, C_(w), determines the magnitude of the AFGA's linearrange.

At FIG. 17B a cross-sectional side view taken along line 17B--17B ofFIG. 17A is shown. The horizontal dimension is roughly to scale andaligned with the layout view of FIG. 17A, however, the vertical scalehas been greatly exaggerated for clarity. All SiO₂ electron transport ispreferably done through high quality, thermally grown gate oxide ratherthan through poorly controlled, deposited interpoly oxide for improvedand consistent performance. The majority of electron tunneling occurs at118 along the edge of the overlap between the floating gate and the n⁺contact in the high-voltage well 120 as shown. The majority ofhot-electron injection occurs in a narrow region 122 in the channel 124of the pFET 116 relatively close to the drain region 126 as shown. Theportion of the floating gate 106a which extends out over the substrate128 to tunneling junction 118 in well 120 should be over field oxide 130in order to minimize the floating-gate-to-substrate capacitance and aidin rejecting power supply noise.

Alternative Embodiments Employing the AFGA

The autozeroing technique used in the autozeroing floating-gateamplifier (AFGA) can be applied to a wide variety of floating-gate MOScircuits (See, for example, B. A. Minch, C. Diorio, P. Hasler, and C. A.Mead, "Translinear Circuits Using Subthreshold Floating-Gate MOSTransistors," Analog Integrated Circuits and Signal Processing, vol. 9,no. 2, 1996, pp. 167-179.) to continuously restore some desired baselineoperation on a slow timescale--on the order of seconds or longer. FIGS.18-25 illustrate some of the floating-gate MOS circuits that we haveconceived of that use this same technique.

FIGS. 18A-B show circuits for two autozeroing photoreceptors: FIG. 18Autilizes a phototransistor 132 and FIG. 18B utilizes a photodiode 134.In each case, an incoming light signal 136 is transduced into aproportional photocurrent. This current is then transformed into anoutput voltage, V_(out), by an autozeroing pFET 138, 140, respectively.These photoreceptors have a logarithmic response to transient changes inintensity; the slope of this response is governed by the ratio C₁ /C₂.Slow variations in the background light intensity are adapted out by theautozeroing behavior.

FIGS. 19A-B show the use of an AFGA with certain generic types ofsensors. Since many sensors transduce a signal as a fractional change intheir resistance, in many cases, the baseline resistance may vary fromsensor to sensor or over time within the same sensor. Placing such asensor 142 between the drain of an autozeroing pFET 144 and ground asdepicted in FIG. 19A results in a circuit that transduces a givenpercentage change in the sensor's resistance into a transient outputvoltage of fixed amplitude. This amplitude can be set by changing theratio C₁ /C₂. Long-term drift in the baseline resistance of the sensoris adapted out by the circuit's autozeroing behavior. If the baselinesensor resistance is less than 1MΩ, the pFET will not be able to supportthe resulting current levels while remaining in its subthreshold(exponential) regime. In this case, an NPN transistor 146 may beinserted as shown in FIG. 19B where the subthreshold current in the pFET148 is multiplied by the NPN transistor's current gain, β, to properlybias the sensor 150. Such devices are particularly well suited tosmell-sensing and chemical sensing devices currently under development.Many such devices are based upon variable sensor resistance andexperience drift over time.

FIG. 20 depicts the circuit of an autozeroing differentiator analogousto the "Diff1" circuit of C. Mead, Analog VLSI and Neural Systems, NewYork, Addison Wesley, 1989. The first AFGA 152 acts as an invertingloss-pass filter whose time-constant is set by V.sub.τ1. The second AFGA154 adds the input signal with the negative low-pass filtered output ofthe first AFGA 152 and multiplies the sum by a gain, -C₁ /C₂. Thus, theoutput voltage, V_(out), is a scaled, high-pass-filtered version of theinput voltage V_(in). When used as a differentiator, V.sub.τ2 isnormally higher relative to ground than V.sub.τ1 so that the second AFGA154 does not low-pass filter the output. However, the circuit may beused as a band-pass filter by making V.sub.τ2 comparable to V.sub.τ1.

FIG. 21 depicts the circuit of a tunable, autozeroing second-orderfilter employing a first, second and third AFGA, 156, 158 and 160,respectively, which can be cascaded to form silicon cochleas. Normallybias voltage V.sub.τ3 is set higher relative to ground than are biasvoltages V.sub.τ1 and V.sub.τ2. The center frequency and quality factorof the filter are respectively set by the average and difference betweenV.sub.τ1 and V.sub.τ2.

FIG. 22 depicts an autoranging winner-take-all (WTA) circuit related tothe current-mode max circuit described in B. A. Minch, C. Diorio, P.Hasler, and C. Mead, "A νMOS Soft-Maximum Current Mirror, " Proceedingsof the 1995 International Symposium on Circuits and Systems, Seattle,Wash., vol. 3, pp. 2249-2252. The circuit of FIG. 22 shows three stages,Stage 1 (162), Stage 2 (164) and Stage N (166). Many more stages couldbe placed between Stage 2 and Stage N if desired. The output voltage ofthe stage with the largest input current will be low whereas the rest ofthe output voltages will be at V_(dd). The charge on the single floatinggate 168 common to all stages governs the range of currents to which thecircuit is sensitive. In this case, the autozeroing behavior adjusts thecharge on the floating gate 168 so that the circuit adjusts its range tomatch the size of the largest current input. The tunneling currentthrough tunneling junction 170 is balanced by an injection current atthe drain of the pFET of the winning stage.

FIG. 23 depicts an autozeroing version of the WTA circuit described inJ. Lazzaro, S. Ryckebusch, M. A. Mahowald, and C. A. Mead,"Winner-Take-All Networks of O(N) Complexity," in D. S. Touretzky, ed.,Advances in Neural Information Processing Systems 1, San Mateo, Calif.:Morgan Kaufmann, 1989, pp. 703-711. This is also an N-stage device withStages 1, 2 and N shown. The outputs may be taken as either voltages orcurrents. In this circuit, V_(b) is used to set the current flow throughpFET 172 which, in turn, sets the total output current available for allN stages. The circuit transiently signals the location of the inputmaking the largest change, making this a WTA circuit with a"conscience". This circuit may find application in attentive sensoryprocessing.

FIGS. 24A-B depict two examples of autozeroing floating-gate MOStranslinear circuits, See B. A. Minch, C. Diorio, P. Hasler, and C.Mead, "Translinear Circuits Using Subthreshold Gloating-Gate MOSCircuits," Analog Integrated Circuits and Signal Processing, vol. 9, no.2, 1996, pp. 167-179. FIG. 24A depicts an autozeroing geometric-meancircuit and FIG. 24B depicts an autozeroing squaring-quotient circuit.All capacitors shown have the same value, C₁.

Here, because a one-half power law is implemented, the drain voltage ofthe first input pFET at node 182 couples to the floating gate 184 of theinput pFET 186 with twice the capacitance (i.e., two capacitors of valueC₁) as it does to the floating gate 188 of the output pFET 174. The sameis true for the second input AFGA 190.

In the circuit of FIG. 24B, a first AFGA 198, a second AFGA 200 and anoutput floating gate pFET 202 are used to implement a squaring power lawand a minus-1 power law as in the relation I_(3out) ˜I_(2in) ^(2/I)_(1in). The drain voltage of the second input pFET 192 is coupled to thefloating gate 194 of output pFET 176 with twice the capacitance as it iscoupled to its own floating gate 196 to implement the squaring powerlaw. First AFGA 198 couples to output floating gate pFET 202 throughinverting unity gain AFGA 200 so as to implement the minus-1 power law.Here the drain 204 of AFGA 198 couples into its own floating gate withtwo capacitors of value C₁ while coupling into the floating gate 194 ofthe output floating gate pFET 176 through the same number of capacitorsof value C₁.

In these circuits, the output current, I_(3out), is proportional to theproduct of powers of the input currents I_(1in) and I_(2in). Theconstant of proportionality is changed by the autozeroing behavior on aslow timescale so that the output current returns to some baselinevalue. Care must be exercised with the output transistors; if the drainof an output transistor is held at a constant voltage (i.e., connectedto a low-impedance load), the floating-gate voltage runs away.Consequently, for the circuits shown, the output pFETs 174, 176 do notautozero and their respective tunneling junctions 178, 180 are eitheromitted or biased so that no significant tunneling takes place.

FIG. 25 depicts a circuit for an autozeroing first-order log-domainfilter. Log-domain filters are discussed, for example, in D. R. Frey,"Log-Domain Filtering: An Approach to Current-Mode Filtering," IEEEProceedings-G, vol. 140, no. 6, 1993, pp. 406-416. The circuit includesthree stages of AFGAs 206, 208, 210 and an output floating gate pFET212. All capacitors from drains to floating-gates have the same valueand should be substantially smaller than C.sub.τ, which has a valuepreferably about ten times that of C₁. The output current lout is alarge-signal-linear, first-order, low-pass-filtered version of the inputcurrent I_(in). The time constant of the filter is proportional toC.sub.τ U_(T) /I.sub.τ. In this case, the autozeroing behavior adaptsthe gain of the filter on a slow timescale so that the DC component ofthe output current remains nearly fixed despite changes in the DC levelof the input current I_(in). Again, care must be exercised with theoutput stage 212; if the drain of the output stage is held at a constantvoltage (i.e., connected to a low-impedance load), the floating-gatevoltage runs away. Consequently, for the circuit shown, the output pFETdoes not autozero and its tunneling junction 214 is either omitted orbiased so that no significant tunneling takes place.

SUMMARY

The AFGA is a simple example of a wide class of adaptive floating-gateMOS circuits; each of these circuits uses tunneling and hot-electroninjection to modulate the charge on floating gates to return the circuitto a baseline condition on a slow timescale. When the appropriate choiceof feedback is applied to the floating gate, this adaptation is aninherent part of the circuit's operation--no additional controlcircuitry is required. In the case of AFGA, the feedback is set up sothat the output voltage returns to its steady-state value on some long(selected) timescale. The modulation of the pFET hot-electron injectionby the output voltage provides the correct feedback to return the outputvoltage to the proper operating regime.

The AFGA has four operating regimes that are similar for biases bothabove and below threshold. First, in the adaptation region, the AFGAbehaves as a high-pass filter at low frequencies, where the timescale isset by the tunneling and injection currents. Second, in the integratingregion, the AFGA behaves as a low-pass filter at high frequencies, wherethe timescale is set by the nFET bias current. Third, the AFGA acts asan amplifier for timescales between the adaptation and integratingregimes. Fourth, at frequencies much higher than the integratingbehavior, the AFGA exhibits capacitive feedthrough, which can be reducedby an increase in either C_(w) or C_(L).

The AFGA is always a first-order system, even in the presence ofparasitic capacitances; therefore, the AFGA is always stable, with 90degrees of phase margin for noninductive loads. Any amplifier withresistive feedback is at least a second-order system, but an amplifierwith capacitive feedback can be a first-order system. For moderateadaptation rates, the low-frequency time constant remains nearlyconstant, and any shift is due primarily to trapping in the tunnelingoxide.

MOS devices and quantum processes, such as electron tunneling andhot-electron injection, are often criticized for their high 1/ƒ noise.Since the AFGA's noise performance is similar in thermal and 1/ƒ noisecharacteristics to that of a standard MOS amplifier, the tunneling andinjection processes do not add appreciable noise to the amplifier. Inaddition, with a desired adaptation rate, the low-frequency noisegenerated in the AFGA can be significantly reduced; such a reductioncannot be obtained in a standard amplifier with a blocking capacitor atthe input. The linear range of the AFGA can be increased by increasingC_(w) ; the dynamic range of the AFGA can be increased by increasingC_(w) or C_(L).

Although illustrative presently preferred embodiments and applicationsof this invention are shown and described herein, many variations andmodifications are possible which remain within the concept, scope, andspirit of the invention, and these variations would become clear tothose of skill in the art after perusal of this application. Theinvention, therefore, is not to be limited except in the spirit of theappended claims.

What is claimed is:
 1. An autozeroing differentiator, comprising:a firstMOS transistor having a first floating gate, a first source and a firstdrain; first means for hot electron injection of electrons onto saidfirst floating gate; first means for Fowler-Nordheim tunneling ofelectrons off of said first floating gate; a second MOS transistorhaving a second floating gate, a second source and a second drain;second means for hot electron injection of electrons onto said secondfloating gate; second means for Fowler-Nordheim tunneling of electronsoff of said second floating gate; a signal input capacitively coupled tosaid first floating gate and said second floating gate; said firstsource and said second source connected to a first power supply set to afirst DC voltage level; said first drain connected to a first circuitnode, said second drain connected to a second circuit node, said firstcircuit node capacitively coupled to said first and second floatinggates and said second circuit node capacitively coupled to said secondfloating gate; a first current source connected to said first circuitnode; a second current source connected to said second circuit node; andsaid second circuit node being a signal output.
 2. An autozeroingdifferentiator according to claim 1, wherein said first and secondcurrent sources are nFET MOS transistors each having a source connectedto a second power supply set to a DC voltage level less than said firstDC voltage level, a gate connected, respectively, to first and secondbias voltage sources, and a drain connected, respectively, to said firstand second circuit nodes.
 3. An autozeroing differentiator according toclaim 2, wherein said first and second MOS transistors are pFETs.
 4. Atunable autozeroing second-order filter comprising:a first MOStransistor having a first floating gate, a first source and a firstdrain; first means for hot electron injection of electrons onto saidfirst floating gate; first means for Fowler-Nordheim tunneling ofelectrons off of said first floating gate; a second MOS transistorhaving a second floating gate, a second source and a second drain;second means for hot electron injection of electrons onto said secondfloating gate; second means for Fowler-Nordheim tunneling of electronsoff of said second floating gate; a third MOS transistor having a thirdfloating gate, a third source and a third drain; third means for hotelectron injection of electrons onto said third floating gate; thirdmeans for Fowler-Nordheim tunneling of electrons off of said thirdfloating gate; a signal input capacitively coupled to said firstfloating gate; said first, second and third source connected to a powersupply set to a first DC voltage level; said first, second and thirddrains connected, respectively, to first, second and third circuitnodes; said first circuit node capacitively coupled to said firstfloating gate and said second floating gate; a signal output coupled tosaid second circuit node; said second circuit node capacitively coupledto said second floating gate and said third floating gate; said thirdcircuit node capacitively coupled to said third floating gate and saidfirst floating gate; and a first, second and third current sourceconnected, respectively, to said first, second and third circuit nodes.5. A tunable autozeroing second-order filter according to claim 4wherein said first, second and third current sources are nFET MOStransistors each having a source connected to a second power supply setto a second DC voltage level less than said first DC voltage level,gates connected, respectively, to first, second and third bias voltagesources, and drains connected, respectively, to said first, second andthird circuit nodes.
 6. A tunable autozeroing second-order filteraccording to claim 5 wherein said first, second and third MOStransistors are pFETs.